Refined Unified Formulation for Efficient Folding and Unfolding Analyses of Slender Thin-Walled Structures

Abstract

We present a high-fidelity refined unified nonlinear finite element formulation for the efficient and robust analysis of slender thin-walled bodies during highly nonlinear deformation. Our formulation utilizes an independent discretization of the displacement field along the beam axis and over the cross section. By matching different refinements in different cross sections, it is able to apply higher-order beam theories in highly deformed regions, to capture complex buckling and postbuckling behavior, whilst retaining the computational efficiency offered by lower refinements elsewhere. The exemplar structure for this paper is the tape spring—a commonly proposed component of deployable structures with ability to combine self-deployment, via a release of stored strain energy, with locking into a relatively stiff geometric configuration with a curved cross section. To simulate localized folds due to a flattening of the cross section, the arc-length method with an automatic increment technique is employed.